{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "UNIT STEP FUNCTION\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'u(t)')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#unit step function\n",
    "import matplotlib.pyplot as p\n",
    "import numpy as np\n",
    "impulse = []\n",
    "LL = -10\n",
    "UL = 10\n",
    "n = np.arange(LL,UL,1)\n",
    "for sample in n:\n",
    "\tif sample >= 0:\n",
    "\t\timpulse.append (1)\n",
    "\telse:\n",
    "\t\timpulse.append (0)\n",
    "p.stem (n, impulse)\n",
    "p.title('Unit Step Function')\n",
    "p.xlabel('t')\n",
    "p.ylabel('u(t)') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "UNIT IMPULSE FUNCTION\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'd(t)')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#unit impulse function\n",
    "import matplotlib.pyplot as p\n",
    "import numpy as np\n",
    "impulse = []\n",
    "LL = -10\n",
    "UL = 10\n",
    "n = np.arange(LL,UL,1)\n",
    "for sample in n:\n",
    "\tif sample == 0:\n",
    "\t\timpulse.append (1)\n",
    "\telse:\n",
    "\t\timpulse.append (0)\n",
    "p.stem (n, impulse)\n",
    "p.title('Unit Impulse Function')\n",
    "p.xlabel('t')\n",
    "p.ylabel('d(t)') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "UNIT RAMP FUNCTION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'r(t)')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#unit ramp function\n",
    "import matplotlib.pyplot as p\n",
    "import numpy as np\n",
    "impulse = []\n",
    "LL = -10\n",
    "UL = 10\n",
    "n = np.arange(LL,UL,1)\n",
    "for sample in n:\n",
    "\tif sample >= 0:\n",
    "\t\timpulse.append (sample)\n",
    "\telse:\n",
    "\t\timpulse.append (0)\n",
    "p.stem (n, impulse)\n",
    "p.title('Unit Ramp Function')\n",
    "p.xlabel('t')\n",
    "p.ylabel('r(t)') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "EXPONENTIAL FUNCTION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'x(t)')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#exponential function\n",
    "import matplotlib.pyplot as p\n",
    "import numpy as np\n",
    "impulse = []\n",
    "LL = 0\n",
    "UL = 15\n",
    "n = np.arange(LL,UL,1)\n",
    "for sample in n:\n",
    "\tif sample >= 0:\n",
    "\t\timpulse.append (sample**3)\n",
    "\telse:\n",
    "\t\timpulse.append (0)\n",
    "p.stem (n, impulse)\n",
    "p.title('Exponential Function')\n",
    "p.xlabel('t')\n",
    "p.ylabel('x(t)') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SINUSOIDAL FUNCTION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x7f5bccfb7250>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "time = np.arange(0, 10, 0.1)\n",
    "amplitude= np.sin(time) \n",
    "plt.plot(time, amplitude)\n",
    "plt.title('Sine wave')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Amplitude = sin(time)') \n",
    "#plt.grid(True, which='both') \n",
    "plt.axhline(y=0, color='black')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
